# The minimal statistical interpretation is neither minimal nor statistical

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• Demystifier
In summary, the Ballentine interpretation is neither minimal nor statistical because it insists that there is no wave function collapse, or state reduction.
Demystifier
Gold Member
Those days I'm in the mood of criticizing the Ballentine's statistical interpretation, also known as the minimal statistical interpretation. Here I will argue that it is, in fact, neither minimal nor statistical.

The main culprit is that Ballentine repeatedly insists that there is no wave function collapse, or state reduction, or whatever one wants to call it. I'm not saying that Ballentine is wrong about that. What I am saying is that an interpretation which insists that there is no collapse is neither minimal nor statistical.

Why is it not minimal? Because a minimal interpretation should be agnostic about any claim that cannot be directly checked by experiments. The Ballentine interpretation is in agreement with experiments, but there are interpretations which claim the existence of collapse, which are in agreement with experiments too. So the truly minimal interpretation would be the purely instrumental interpretation which is agnostic on the existence of collapse. The Ballentine interpretation is not agnostic, hence it's not minimal.

Why is it not statistical? In the purely statistical interpretation, where the wave function is just a probability amplitude and nothing else, the collapse obviously exists. That's because the probability (conditional probability, to be more precise) suddenly changes when new information (about the measurement outcome) arrives. Therefore the state, which is nothing but the probability amplitude, suddenly changes as well, and this sudden change is called collapse (or state reduction). So the interpretation which insists that there is no collapse is not purely statistical.

So what is the Ballentine interpretation really? It's hard to tell. It's some incoherent mixture of pure instrumentalism and implicit additional variables interpretation, in which explicit talk about additional variables is forbidden (because there is no explicit experimental evidence for their existence). I would describe it as what remains when one first starts with a Bohmian interpretation, then integrates out (averages over) all the unknown details of microscopic Bohmian beables, and finally gets confused by trying to completely forget the Bohmian beables.

EDIT: After a long discussion, in the post
https://www.physicsforums.com/threa...r-minimal-nor-statistical.998661/post-6450421
I have concluded that the so-called "minimal" interpretation is in fact the maximal interpretation, or maximal denial interpretation to be more precise.

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bhobba, Delta2, Lord Jestocost and 2 others
Well, these statements are also interpretation dependent themselves.

Concerning the first part, I would say that to have a collapse you go beyond pure interpretation but you need a true extension of QT which involves a collapse, because in standard QT there is no collapse in the dynamics. A well-known example for such an extension of QT is GRW (Ghirardi-Rimini-Weber model).

The 2nd part you seem to follow a Bayesian interpretation of probabilities and insist on knowing how to describe the system after the measurement (which indeed is what the collapse/state reduction is needed for). I'm a bit easier satisfied by just taking the QT formalism as a prediction for the probabilities given a preparation of the measured system and I don't care what happens to this system after I'm done with all observations on it.

The next unsharp notion is "beable". What's precisely meant by "beable"? Is it the outcome of a measurement (i.e., the macroscopically readable pointer position of the device)?

I think at the end I end up with "shutup and calculate", because it seems to be easier to understand how QT is applied to real-world experiments than to find a watertight and well-defined interpretation of the formalism. Then the honest way is to state that the way physicists interpret the formalism in concrete applications is all there is and that we are unable to find an agreement for a general formulation that is acceptable to a majority of quantum physicists.

bhobba
Isn't the "minimal point" of associating the wavefunction with the ensemble, because that is how actual experiements corroborate quantum theory.

(An agent can certainly USE probabilistic models to "place bets" in individual situations, but one can not infer a confident probability from single interaction!)

Also, isn't it statistical as the probability refers not the ensemble, rather than single observabtion. The probability of the ensemble stays the same, its not affected by single samples? Also the experiment is "terminal". What happens after observation is not part of theory(*). QM describes only the best expectation of what happens - in between - preparation and observation, in terms of statistics.

Also, if you think about how the state of the detector may collapse, then we are changing the cut. I find this to be a constant source of confusion. As many problem are associated precisely with the choice of cut, it is no solution to just move the cut. Then we can have the same principal problem at the new cut!

(*) To really ask what the state is after interaction in single cases, we are getting to the interesting questions, but this i consider to be an open question that none of the interpretations present a solution to. We need revision of theory not just interpreation. IMO to meaningfully talk about state after measurment the observer must enter the picture as an agent participating. But we have no theory for this.

/Fredrik

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vanhees71 said:
I think at the end I end up with "shutup and calculate"
I think your interpretation would be better described as "shut up during calculation, but talk a lot when get bored by calculation".

akhmeteli, AlexCaledin, bhobba and 1 other person
I always thought the minimal interpretation was the "shut up and calculate" interpretation: If you set up an ensemble of identically prepared systems and specify a measurement procedure that generates data, QM will report the frequencies and correlations that will be present in the data.

mattt, bhobba, dextercioby and 1 other person
Demystifier said:
Those days I'm in the mood of criticizing the Ballentine's statistical interpretation,...

To my mind, Abner Shimony has said the essential about Ballentine’s “interpretation”. Maybe, Ballentine has confused himself. As Abner Shimony remarks in “Symposia on the Foundations of Modern Physics 1992 - The Copenhagen Interpretation and Wolfgang Pauli” (edited by K. V. Laurikainen and C. Montonen):

There is, for example, Ballentine, whom I mentioned yesterday. He says: ‘I am not a hidden variable theorist, I am only saying that quantum mechanics applies not to individual systems but to ensembles.’ I didn't put this down separately because I simply do not understand that position. Once you say that the quantum state applies to ensembles and the ensembles are not necessarily homogeneous you cannot help asking what differentiates the members of the ensembles from each other. And whatever are the differentiating characteristics those are the hidden variables. So I fail to see how one can have Ballentine's interpretation consistently. That is, one can always stop talking and not answer questions, but that is not the way to have a coherent formulation of a point of view. But to carry out the coherent formulation of a point of view, as I think Einstein had in mind, you certainly have to supplement the quantum description with some hypothetical extra variables.” [bold by LJ]

Delta2
Lord Jestocost said:
To my mind, Abner Shimony has said the essential about Ballentine’s “interpretation”. Maybe, Ballentine has confused himself. As Abner Shimony remarks in “Symposia on the Foundations of Modern Physics 1992 - The Copenhagen Interpretation and Wolfgang Pauli” (edited by K. V. Laurikainen and C. Montonen):

There is, for example, Ballentine, whom I mentioned yesterday. He says: ‘I am not a hidden variable theorist, I am only saying that quantum mechanics applies not to individual systems but to ensembles.’ I didn't put this down separately because I simply do not understand that position. Once you say that the quantum state applies to ensembles and the ensembles are not necessarily homogeneous you cannot help asking what differentiates the members of the ensembles from each other. And whatever are the differentiating characteristics those are the hidden variables. So I fail to see how one can have Ballentine's interpretation consistently. That is, one can always stop talking and not answer questions, but that is not the way to have a coherent formulation of a point of view. But to carry out the coherent formulation of a point of view, as I think Einstein had in mind, you certainly have to supplement the quantum description with some hypothetical extra variables.” [bold by LJ]
Here the confusion arrises from two different meanings of "hidden variables". Ballentine means deterministic hidden variables, while Shimony means additional variables.

Fra
I was about to make a similar comment as above: To assume that an "unpredictable phenomenon" means there has to exist hidden variables, that via some unknown but assumed deterministic laws could recover predictability is a wild and strong assumption.

As someone that has a kind of interacting agent view of this, there is for me inly ONE kind of "hidden variables" that IMO is interesting. And interetingly Demystifier wrote a paper on this in the past.

Solipsistic hidden variables, Hrvoje Nikoli ́c
"We argue that it is logically possible to have a sort of both reality and locality inquantum mechanics. To demonstrate this, we construct a new quantitative modelof hidden variables (HV’s), dubbed solipsistic HV’s, that interpolates between theorthodox no-HV interpretation and nonlocal Bohmian interpretation. In this model,the deterministic point-particle trajectories are associated only with the essentialdegrees of freedom of the observer, and not with the observedobjects. In contrastwith Bohmian HV’s, nonlocality in solipsistic HV’s can be substantially reduceddown to microscopic distances inside the observer. Even if such HV’s may look philosophically unappealing to many, the mere fact that they are logically possibledeserves attention."
-- https://arxiv.org/pdf/1112.2034.pdf

This idea in the interacting agent view I am has the potenetial to conceptually explains why the hidden variables can never recover predictability in the ansatz assume in bell theorem etc. The hidden variables could simply be the agents "real physical internal information" about the environment. But this is inaccesssible to other agents, in all other ways except they can try to infer it via interactions. This means interactions themselves are even partially explained by the hidden variables. It can be thought of as local as well, since the agents responds only to LOCALLY available "real" information. The "real" info is hidden beacuse it takes a real physical interaction to "infer it".

Contrary to what Demystifier writes in bold above, I think this KIND of "hidden variables" are VERY appealing,and it interesting in the sense that it allowd a common junction between two on the surface opposite traditions of intepreting QM: "hidden variable seekers" and "solipsists" :)

/Fredrik

Demystifier and atyy
Well, I disagree.
Demystifier said:
Why is it not minimal? Because a minimal interpretation should be agnostic about any claim that cannot be directly checked by experiments. The Ballentine interpretation is in agreement with experiments, but there are interpretations which claim the existence of collapse, which are in agreement with experiments too. So the truly minimal interpretation would be the purely instrumental interpretation which is agnostic on the existence of collapse. The Ballentine interpretation is not agnostic, hence it's not minimal.
Being agnostic is not an option, because in the statistical interpretation, there cannot be a collapse (see below). So it is minimal, because you cannot make it any smaller.
Demystifier said:
Why is it not statistical? In the purely statistical interpretation, where the wave function is just a probability amplitude and nothing else, the collapse obviously exists. That's because the probability (conditional probability, to be more precise) suddenly changes when new information (about the measurement outcome) arrives. Therefore the state, which is nothing but the probability amplitude, suddenly changes as well, and this sudden change is called collapse (or state reduction). So the interpretation which insists that there is no collapse is not purely statistical.
I would say that obviously there is no collapse. After the update you no longer have a representative of the original ensemble. It is now an element of a different ensemble. It makes no sense to even talk about collapse. The wave function before what you call the collapse, is the state of an ensemble of equally prepared systems in a specific way. After that, you no longer have one of them, so the wave function didn't collapse. You may insist on calling this collapse as well, but then it will be very different to what you actually mean.

Fra and vanhees71
martinbn said:
You may insist on calling this collapse as well, but then it will be very different to what you actually mean.
And what do I actually mean?

vanhees71
Demystifier said:
And what do I actually mean?
That the state is different after the measurement. It changed from whatever it was, to something else.

martinbn said:
I would say that obviously there is no collapse. After the update you no longer have a representative of the original ensemble. It is now an element of a different ensemble. It makes no sense to even talk about collapse. The wave function before what you call the collapse, is the state of an ensemble of equally prepared systems in a specific way. After that, you no longer have one of them, so the wave function didn't collapse. You may insist on calling this collapse as well, but then it will be very different to what you actually mean.

Well, the insistence that the original ensemble still evolves unitarily is then a claim which is "unobservable".

And it is also unclear how one can even have the state of a sub-ensemble, when there is no assumption giving that in Balletine's interpretation. Ballentine has not defined sub-ensembles, and mathematically he needs to because a mixed quantum state does not have a unique decomposition into sub-ensembles. If the sub-ensembles existed before hand, then his interpretation is Many Many Worlds. If they did not exist before hand, then he needs to define them.

I would say Ballentine's interpretation is simply not quantum mechanics.

The minimal interpretation does not claim that the ensemble evolves unitarily. When interacting with something else, it becomes an open quantum system, and what evolves unitarily is the full system consisting of the measured system and the measurement device. This IS quantum mechanics.

The minimal interpretation does not make a collapse assumption nor a "Heisenberg cut". It's clear that these are non-minimal interpretational additions to the formalism of quantum mechanics as a physical theory. Not even all Copenhagen proponents were insisting on a collapse.

atyy said:
Well, the insistence that the original ensemble still evolves unitarily is then a claim which is "unobservable".
There is no such thing as the "ensemble evolves". The state evolves.
And it is also unclear how one can even have the state of a sub-ensemble, when there is no assumption giving that in Balletine's interpretation. Ballentine has not defined sub-ensembles, and mathematically he needs to because a mixed quantum state does not have a unique decomposition into sub-ensembles. If the sub-ensembles existed before hand, then his interpretation is Many Many Worlds. If they did not exist before hand, then he needs to define them.
This is to general. Can you give an example where one needs subensembles.

martinbn said:
There is no such thing as the "ensemble evolves". The state evolves.

No. The state does not evolve in the Heisenberg picture in Ballentine's interpretation. Do you claim that the Schroedinger picture is more correct? Of course, the state evolves in both pictures if you admit a collapse.

martinbn said:
This is to general. Can you give an example where one needs subensembles.

In post #9, you said " After the update you no longer have a representative of the original ensemble. It is now an element of a different ensemble". The "different ensemble" is a subensemble of the original ensemble.

QT is picture independent. The physical quantity that "evolves" are the probabilities for the outcome of measurements.

If you can describe a state to the system after having interacted with the measurement device, i.e., after separating the system again from interacting with the device (and "the environment") you've prepared the system again in a new state, and repeating this same procedure to many systems, you've prepared a new ensemble.

atyy said:
No. The state does not evolve in the Heisenberg picture in Ballentine's interpretation. Do you claim that the Schroedinger picture is more correct? Of course, the state evolves in both pictures if you admit a collapse.
Of course in the Heisenberg picture the observables evolve. The point was that "the ensemble evolves" is unclear. The ensemble is not a mathematical object to be subject to differential equations. So, what did you mean?
In post #9, you said " After the update you no longer have a representative of the original ensemble. It is now an element of a different ensemble". The "different ensemble" is a subensemble of the original ensemble.
No, it is not. Here is an example. Prepare a 1/2-spin system in the state |up>. The ensemble is all equaly prepared systems, and the state describes the ensemble. Measure allong the horizontal axis, and say you get "right" as an outcome. If you continuou to study the system, now it belongs to an ensemble described in the state |right>. This ensemble includes all systems that are preapred in that state, whether they came from the measurment you just did or in any other way.

p.p. I am not very precise in using the word state, I hope it is not confusing. I am not used to the statistical interpretation language.

martinbn said:
Being agnostic is not an option, because in the statistical interpretation, there cannot be a collapse (see below). So it is minimal, because you cannot make it any smaller.

One should clearly define what the term “statistical interpretation” means. In case one uses the term “statistical interpretation” as a synonym for “ensemble interpretation”, one is on the wrong road when calling it “minimal”.

Cord Friebe, Holger Lyre, Manfred Stöckler, Meinard Kuhlmann, Oliver Passon and Paul M. Näger in “The Philosophy of Quantum Physics”:

“If one tries to proceed systematically, then it is expedient to begin with an interpretation upon which everyone can agree, that is with an instrumentalist minimal interpretation. In such an interpretation, Hermitian operators represent macroscopic measurement apparatus, and their eigenvalues indicate the measurement outcomes which can be observed, while inner products give the probabilities of obtaining particular measured values. With such a formulation, quantum mechanics remains stuck in the macroscopic world and avoids any sort of ontological statement about the (microscopic) quantum-physical system itself.

Going one step further, we come to the ensemble interpretation:
Here, the mathematical symbols indeed refer to microscopic objects, but only to a very large number of such systems. According to this view, quantum mechanics is a kind of statistical theory whose laws are those of large numbers. In regard to a particular system, this interpretation remains agnostic.” [Italics in original, bold by LJ]

AlexCaledin
martinbn said:
No, it is not. Here is an example. Prepare a 1/2-spin system in the state |up>. The ensemble is all equaly prepared systems, and the state describes the ensemble. Measure allong the horizontal axis, and say you get "right" as an outcome. If you continuou to study the system, now it belongs to an ensemble described in the state |right>. This ensemble includes all systems that are preapred in that state, whether they came from the measurment you just did or in any other way.

And what has happened to the state? Is it still evolving unitarily? Is any state still evolving unitarily?

What happens to the system depends on the specifics of the measurement. When doing an SGE in ##x## direction and just blocking one of the partial beams (say the outcomes "left") you prepared a new ensemble in the state ##|\text{Right} \rangle \langle \text{Right}|##. It's the paradigmatic ensemble for a preparation by filtering (often called a "von Neumann filter measurement").

This is of course not a unitary time evolution, because the particle is interacting with the filter. Only the particle+filter system evolves unitarily.

Lord Jestocost said:
One should clearly define what the term “statistical interpretation” means. In case one uses the term “statistical interpretation” as a synonym for “ensemble interpretation”, one is on the wrong road when calling it “minimal”.

Cord Friebe, Holger Lyre, Manfred Stöckler, Meinard Kuhlmann, Oliver Passon and Paul M. Näger in “The Philosophy of Quantum Physics”:

“If one tries to proceed systematically, then it is expedient to begin with an interpretation upon which everyone can agree, that is with an instrumentalist minimal interpretation. In such an interpretation, Hermitian operators represent macroscopic measurement apparatus, and their eigenvalues indicate the measurement outcomes which can be observed, while inner products give the probabilities of obtaining particular measured values. With such a formulation, quantum mechanics remains stuck in the macroscopic world and avoids any sort of ontological statement about the (microscopic) quantum-physical system itself.

Going one step further, we come to the ensemble interpretation:
Here, the mathematical symbols indeed refer to microscopic objects, but only to a very large number of such systems. According to this view, quantum mechanics is a kind of statistical theory whose laws are those of large numbers. In regard to a particular system, this interpretation remains agnostic.” [Italics in original, bold by LJ]
Interesting formulation too (technically of course instead of Hermitian it must read self-adjoint), but here I have the objection that not all measurement apparati are ideal ones and thus do not need to get only eigenvalues of the operator describing the measured observable but also the macrocopic measurement outcomes come with some uncertainty ("statistical error") and finite resolution ("systematic error").

The ensemble interpretation has the advantage that, as described in the quote above, here the formalism refers to the "microscopic objects", and the statistical nature of the prediction directly refers to the empirical observation that the outcome of measurements on "completely prepared" (i.e., prepared in a pure state) systems are random with a probability/statistics being successfully predicted by QT.

vanhees71 said:
What happens to the system depends on the specifics of the measurement. When doing an SGE in ##x## direction and just blocking one of the partial beams (say the outcomes "left") you prepared a new ensemble in the state ##|\text{Right} \rangle \langle \text{Right}|##. It's the paradigmatic ensemble for a preparation by filtering (often called a "von Neumann filter measurement").

Sure, but in the more general formalism there is still a state reduction.

vanhees71 said:
This is of course not a unitary time evolution, because the particle is interacting with the filter. Only the particle+filter system evolves unitarily.

That's the claim. Show it.

I think the mistake you are making here is one that Phil Anderson made. It's funny that the chiral anomaly statistically causes a certain sort of interest in quantum foundations.

https://arxiv.org/abs/quant-ph/0112095
Why Decoherence has not Solved the Measurement Problem: A Response to P. W. Anderson
We discuss why, contrary to claims recently made by P. W. Anderson, decoherence has not solved the quantum measurement problem.

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vanhees71 said:
The minimal interpretation does not claim that the ensemble evolves unitarily. When interacting with something else, it becomes an open quantum system, and what evolves unitarily is the full system consisting of the measured system and the measurement device. This IS quantum mechanics.
But in this case its a new system, enlarged. And a new observer. If one is to refrain from the temptation to explain the problem of the cut, but just moving it, i think its better to say to just settle with that it evolves unitarily in between interactions and that's it.

I think a "minimal view" should be that the observed system is (by the observer) expected to evolve unitarily in between measurements. I think the minimal view should not speak about anything else.

To have an expectation of how ANOTHER observer, revises his state, after his measurement is a different question, applied by iteration. Then we are putting behaviour (and thus hamiltoninan) of another observer on the same footing as physical interactions? But for this to be a satisfactory explanation one must study what happens if we keep the iteration? The observer are eventually put outwards, and the quantum system grows bigger and bigger and eventulally pushed out into deep space horizon, and the "system" is all the inteorior. Is this a good abstraction?

/Fredrik

vanhees71 said:
The ensemble interpretation has the advantage that ...

It is as it is. In case you leave the instrumentalist's point of view, you start to make "ontological statements". "The ensemble interpretation has the advantage that...": One can beat about the bush, but at the end these "ontological statements" must be proved by means of experiments.
Is there anything in the formalism of quantum theory which points into the direction of the "ensemble interpretation"? Nothing! To my mind, physicists should not insist on thinking about quantum phenomena with classical ideas. As V. A. Fock warns:

The deeper reason for the circumstance that the wave function cannot correspond to any statistical collective [aka ‘ensemble’, LJ] lies in the fact that the concept of the wave function belongs to the potentially possible (to experiments not yet performed), while the concept of the statistical collective belongs to the accomplished (to the results of experiments already carried out).

(V. A. Fock, “ON THE INTERPRETATION OF QUANTUM MECHANICS”, Czech J Phys (1957) 7: 643)

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atyy said:
And what has happened to the state? Is it still evolving unitarily? Is any state still evolving unitarily?
The state of what?

martinbn said:
No, it is not. Here is an example. Prepare a 1/2-spin system in the state |up>. The ensemble is all equaly prepared systems, and the state describes the ensemble. Measure allong the horizontal axis, and say you get "right" as an outcome. If you continuou to study the system, now it belongs to an ensemble described in the state |right>. This ensemble includes all systems that are preapred in that state, whether they came from the measurment you just did or in any other way.

p.p. I am not very precise in using the word state, I hope it is not confusing. I am not used to the statistical interpretation language.

Ballentine uses the term "subensemble" on in Chapter 9.

Lord Jestocost said:
To my mind, Abner Shimony has said the essential about Ballentine’s “interpretation”.

Once you say that the quantum state applies to ensembles and the ensembles are not necessarily homogeneous you cannot help asking what differentiates the members of the ensembles from each other. And whatever are the differentiating characteristics those are the hidden variables.

Information needed to discriminate members of an ensemble as distinct and unique events need not do so in a systematic manner - and in everyday practice it doesn't.

For example, if we describe a coin toss in an experiment testing a theory of coin tossing by giving the values of variables relevant to the theory ( diameter of coin, location of center of mass, etc.) and also state the outcome of the toss (e.g. Heads), we still may not have enough information to identify exactly one event. To do that, we may need additional information that, from the viewpoint of the theory, is irrelevant. For example, we might be able to use the date, time, and location of the toss to identify it as a unique event. Less systematically, a person could describe a particular toss as "The fifth one we did on the day when the professor wore a green suit"

So, from an abstract point of view, to say that ensembles exist and are "not necessarily homogeneous" does not imply that hidden variables exist. Information sufficient to discriminate individual members of the ensemble may be useless in formulating any theory about the ensemble.

(I don't recall any discussions on the forum of the question "Do unique events exist? " - i.e. Is there a set of physical variables that can always be used to describe a unique event? I think of time-and-place as sufficient information to identify a unique macroscopic event. However, exact time and exact place don't identify a macroscopic property! )

bhobba
Lord Jestocost said:
The deeper reason for the circumstance that the wave function cannot correspond to any statistical collective [aka ‘ensemble’, LJ] lies in the fact that the concept of the wave function belongs to the potentially possible (to experiments not yet performed), while the concept of the statistical collective belongs to the accomplished (to the results of experiments already carried out).

(V. A. Fock, “ON THE INTERPRETATION OF QUANTUM MECHANICS”, Czech J Phys (1957) 7: 643)
Not sure i follow the argument...Did Fock have an issue with relating what's possible, given what is known?

That's what physics is all about: to find the best possible prediction of the future, given knowledge of the present (&past possibly implicit).

In cases where we(for whatever reason) can only predict probability determiniatically, it can not be applied exactly in the single sample game. Ensembles are just practical and probably the simpleat way to approximate probability with real world of finite samples when it comes to corroboration.

But just as one can not determine a probabilty of an outcome from a few samples, one can not determine the initially prepared ensemble from a few single preparation interactions.

This is one of the reasons one can not in practice corroborate any theory of this form for any process that is not arbitrarily repeatable. Its only for processes on both short time and legthscale (ie subatomic physics). So it should be no surprise that we average away the cosmological flow of time in all such theories. Time can by construction play no orher role in such theories than independent parameter.

To imagine cosmological ensembles would make much less sense.

So while i think the statistical view is generally wrong(thinking of toe etc), it seems correct and sound for qm as it stands.

/Fredrik

atyy said:
Ballentine uses the term "subensemble" on in Chapter 9.
Yes, he does use it, four times. But in that same paragraph he points out that the filter type measurements have to be considered a preparation of a new state. He doesn't talk about a state that changes after the filtering, but about the preparation of a new state. If you prefer you can use the word subensemble, but it is limited to only this type of filtering and it changes nothing. I stand by what I wrote.

martinbn said:
Yes, he does use it, four times. But in that same paragraph he points out that the filter type measurements have to be considered a preparation of a new state. He doesn't talk about a state that changes after the filtering, but about the preparation of a new state. If you prefer you can use the word subensemble, but it is limited to only this type of filtering and it changes nothing. I stand by what I wrote.

Regardless, the vast majority of quantum mechanics books have state reduction. And of course state reduction is only needed for selective measurements, which are a form of preparation.

What is the operational interpretation of probability in QM? Choose whatever interpretation you favor.

bhobba
atyy said:
Regardless, the vast majority of quantum mechanics books have state reduction. And of course state reduction is only needed for selective measurements, which are a form of preparation.
Yes, but the topic here is the minimal statistical interpretation.

martinbn said:
That the state is different after the measurement. It changed from whatever it was, to something else.
But why exactly it changes, in my opinion?

mattt
Demystifier said:
But why exactly it changes, in my opinion?
Are you asking me?! The point was that in the statistical interpretation you cannot say that.

martinbn said:
Yes, but the topic here is the minimal statistical interpretation.

Well, you can make up your own mind whether the "ensemble" interpretation is powerful enough to change the mathematics of quantum theory.

IIRC, when @bhobba and I discussed, although he is a fan of Ballentine while I am not, bhobba's own Ensemble interpretation includes a postulate equivalent to state reduction, which is that one can at the end of decoherence in a measurement take the reduced density operator to be ignorance interpretable.

Also, the argument against state reduction is incomprehensible if one takes an operational view of quantum theory. In an operational view, who cares what absurdities happen to the state, since it is not necessarily real and just a tool to calculate the probabilities of measurement outcomes.

That @vanhees71 cares about "causality" (about which he is confused) shows that he thinks the quantum state is real, which would also make the objection to state reduction sensible. Very few people would consider such an interpretation to be minimal.

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